Hybridized gated recurrent unit with variational mode decomposition and an error compensation mechanism for multi-step-ahead monthly rainfall forecasting.

Highly accurate monthly rainfall predictions can provide early warnings for rain-related disasters, such as floods and droughts, and allow governments to make timely decisions. This paper proposes a two-phase error compensation model based on a gated recurrent unit (GRU), variational mode decomposition (VMD), and error compensation mechanism (ECM) (GRU-VMD-ECM) for accurate multi-step-ahead monthly rainfall forecasts. In the first phase, the GRU model is used to make an initial monthly rainfall prediction, and the error series is extracted. In the second phase, the error series is decomposed into eight subseries using the VMD method. Each subseries is then input into the GRU model to build different forecasting models. These predicted error sequences are added to the initial prediction results to obtain the final forecast. The model's performance is tested using six evaluation indicators based on Beijing's monthly rainfall data from 1951 to 2018. The results show that the error compensation mechanism significantly improved the prediction accuracy, particularly in the Nash-Sutcliffe efficiency (NSE) of single-step-ahead prediction which recorded a substantial increase of 281.16% from 0.259981 to 0.990944, as well as a decrease in root mean square error (RMSE) from 2.257580 to 0.249746. Furthermore, the GRU-VMD-ECM model outperforms the RF, GRU-CNN, and VMD-GRU models in terms of precision across all forecasting horizons. These findings highlight the potential of the GRU-VMD-ECM model in providing highly accurate monthly rainfall predictions for early warnings and informed decision-making by governments.